A 2-kg block slides on a frictionless horizontal surfac

A 2-kg block slides on a frictionless horizontal surface and is connected on one side to a spring (k=40 N/m) as shown in the figure. The other side is connected via a massless rope to a 4-kg block that hangs vertically. The system starts from rest with the spring unextended. a)What is the maximum extension of the spring? b)What is the speed of the 4-kg block when the extension is 50 cm? hint: solve using energy not forces -make sure you account for all kinetic and potential energies in the system (you can set the zero of potential energy at different heights for the two masses)
On July 25 1956 the liner Andrea Doria of mass 4.1 x 10^7 kg was heading west at 40 km/hr. It collided off Nantucket Island with the Stockholm of mass 1.7 x 10^7 kg sailing at 30 km/hr in the direction 20 degrees east of north. The bow of the Stockholm temporarily lodged in the side of the Andrea Doria; that is the collision was perfectly inelastic. a)Find their common velocity (speed and direction) just after the collision. b)What was the loss in kinetic energy due to the collision? hint: draw a diagram and pay attention to directions and components (remember the inverse tangent function on your calculator does not always give the correct angle)
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